Lesson objective: Understand that fractions are equivalent if they represent the same amount or name the same location on a number line.

Students bring prior knowledge that fractions are numbers that can be located on a number line, that the denominator tells how many equal sized pieces the whole has been divided into, and that the numerator tells how many parts of that size we are counting (3.NF.A.2). This prior knowledge is extended to equivalent fractions as students examine the locations of two or more fractions on number lines. A conceptual challenge students may encounter is understanding that different fractions can represent the same location on a number line.

The concept is developed through work with a number line, which reinforces the understanding that a fraction is a number.

This work helps students deepen their understanding of equivalence because different fractions that name the same amount of area or the same location on a number line have the same value.

Students engage in Mathematical Practice 4 (model with mathematics) as they represent fractions as numbers on a number line and write equations to show that fractions are equivalent.

**Key vocabulary:**

- equivalent
- number line
- partition

**Special materials needed:**

- one copy of the task for each student